Rigidity percolation and frictional jamming

Silke Henkes (University of Bristol)

Frictional jamming is poorly understood compared to frictionless jamming, however it is arguably more relevant to real-world situations. In this talk, I will introduce an adaptation of rigidity percolation to frictional packings and show that it can predict the location of the transition. This (3,3) pebble game, valid in two dimensions where each particle has three degrees of freedom, takes into account that frictional forces contribute two constraints to each packing, while sliding contacts only contribute one.
Beginning with slowly sheared simulations of two dimensional frictional packings, we show that a percolating rigid cluster emerges when the jamming transition is crossed, and that local forces correlate with the clusters. For real experimental packings, we also find that jamming and the appearance of a percolating rigid cluster correspond with each other. Using the normal modes extracted from the dynamical matrix confirms our identification of coexisting rigid and floppy regions.
In parallel, using a simplified network model of frictional packings, we show that frictional rigidity percolation is a second order transition with exponents distinct from ordinary rigidity percolation. Finally, we construct a new algorithm to create minimal spanning rigid clusters, minimal rigidity proliferation, which points to deep connections between different classes of percolation.